Template:Kronecker

The following documentation is located at Template:Kronecker/doc. [<Edit> Template:Kronecker/doc]
[⧼Purge⧽ Template:Kronecker]

The {{Kronecker}} (or {{Kron}}) mathematical formatting template gives an HTML+CSS or a LaTeX formatted Kronecker symbol.

Usage

{{Kron|nonzero integer|modulo}}

or

{{Kron|nonzero integer|modulo|format}}

where format is taken from

• htm: text style HTML+CSS Kronecker symbol (default);
• HTM: display style HTML+CSS Kronecker symbol;
• tex: text style LaTeX Kronecker symbol;
• TEX: display style LaTeX Kronecker symbol;

Examples

The code (see Kronecker symbol)

The '''Kronecker symbol''' {{math|{{Kron|''a''{{sp|1}}|''n''{{sp|1}}}}|tex = {{Kron|a|n|tex}}|&}} is defined as{{nl|1.35}} 

: {{math|{{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''n''{{sp|1}}|HTM}} {{sp}}{{rel|def}}{{sp}} {{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''u''{{sp|1}}|HTM}} <!--
-->{{sp|1}}{{prod|''i''{{=}}1|''{{Gr|omega}}''{{sp|1}}(''n'')|HTM}} {{Kron|''a''|{{sp|2}}''p{{sub|i}}''{{sp|1}}|HTM}}{{^|{{^|{{^|''e''{{sub|''i''}}|100%}}|100%}}}},
|tex = {{Kron|a|n|TEX}} := {{Kron|a|u|TEX}} \prod_{i=1}^{\omega(n)} {{Kron|a|p_i|TEX}}^{e_i},|&&}}

yields the HTM+CSS

The Kronecker symbol

(a  | n )

is defined as

a   n   :=   a   u      ω (n) ∏   i  = 1    a   pi     ei,

The code

The '''Kronecker symbol''' {{math|{{Kron|''a''{{sp|1}}|''n''{{sp|1}}}}|tex = {{Kron|a|n|tex}}|$}} is defined as{{nl|1.35}} 

: {{math|{{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''n''{{sp|1}}|HTM}} {{sp}}{{rel|def}}{{sp}} {{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''u''{{sp|1}}|HTM}} <!--
-->{{sp|1}}{{prod|''i''{{=}}1|''{{Gr|omega}}''{{sp|1}}(''n'')|HTM}} {{Kron|''a''|{{sp|2}}''p{{sub|i}}''{{sp|1}}|HTM}}{{^|{{^|{{^|''e''{{sub|''i''}}|100%}}|100%}}}},
|tex = {{Kron|a|n|TEX}} := {{Kron|a|u|TEX}} \prod_{i=1}^{\omega(n)} {{Kron|a|p_i|TEX}}^{e_i},|$$}}

yields the LaTeX

The Kronecker symbol $\textstyle {(a\mid n)}$ is defined as

${\begin{array}{l}\displaystyle {\left({\frac {a}{n}}\right):=\left({\frac {a}{u}}\right)\prod _{i=1}^{\omega (n)}\left({\frac {a}{p_{i}}}\right)^{e_{i}},}\end{array}}$